{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Central Limit Theorem and Continuous Probability Distributions\n",
    "\n",
    "Run the code in each of the cells below. Since this is a demonstration, you do not need to add any code. \n",
    "\n",
    "You have an understanding of discrete probability distributions and how they apply to self-driving cars. Now you will gain intuition about one of the most important continuous probability distributions. \n",
    "\n",
    "There is a specific continuous probability distribution that comes up time and time again when working with self-driving cars: the normal distribution (aka Gaussian Distribution). \n",
    "\n",
    "The normal distribution has a special characteristic in that the mean, median and mode are all the same. Run the code in the next cell to see what a normal distribution looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda2\\lib\\site-packages\\ipykernel_launcher.py:19: MatplotlibDeprecationWarning: scipy.stats.norm.pdf\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xa02e588>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import libraries used in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "from matplotlib import mlab\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Set figure height and width\n",
    "fig_size = plt.rcParams[\"figure.figsize\"]\n",
    "fig_size[0] = 8\n",
    "fig_size[1] = 6\n",
    "plt.rcParams[\"figure.figsize\"] = fig_size\n",
    "\n",
    "x = np.linspace(-12, 12, 100)\n",
    "plt.title('Normal distribution \\n mean = 0 \\n standard deviation = ' + str(3))\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('distribution')\n",
    "plt.plot(x,mlab.normpdf(x, 0, 3))    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Like in a discrete probability distribution, the area under the curve represents probability. The difference between a discrete distribution and a continuous distribution is the lack of sudden jumps in the continuous distribution.\n",
    "\n",
    "In self-driving cars, the normal distribution is especially important when detecting other vehicles, pedestrians, animals, bicycles, etc. \n",
    "\n",
    "Say there is a bicycle moving around your self-driving car. \n",
    "\n",
    "A radar measurement might tell you there is a bicycle 10 feet in front of the car, but there is some uncertainty in that measurement. The uncertainty is generally modeled with a normal distribution. \n",
    "\n",
    "In between radar measurements, the self-driving car still needs to be aware of the bicycle's location. So the car will extrapolate where it thinks the bicycle is moving. The uncertainty in the bicycle's location will also be modeled with a normal distribution.\n",
    "\n",
    "![title](bicycle.jpg)\n",
    "\n",
    "The bicycle is most likely in the center of the distribution, but there is still some probability that the bicycle is higher or lower according to the normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Normal Distribution Intuition\n",
    "\n",
    "Compared to some other continuous probability distributions, the normal distribution is relatively easy to work with. And the distribution works well when modelling uncertainty in sensor measurements and object detection.\n",
    "\n",
    "In the Kalman Filter lessons, you will learn more about the characteristics of the distribution and see how to work with it. For now, you'll use this demo to gain intuition about the normal distribution. \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probability Distributions\n",
    "\n",
    "Before you start the demo, let's look at a few examples of probability distributions. Run the code below to visualize a few common continuous probability distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda2\\lib\\site-packages\\ipykernel_launcher.py:4: MatplotlibDeprecationWarning: scipy.stats.norm.pdf\n",
      "  after removing the cwd from sys.path.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-12, 12, 100)\n",
    "\n",
    "plt.subplot(221)\n",
    "plt.plot(x,mlab.normpdf(x, 0, 3)) \n",
    "plt.title('Normal Distribution')\n",
    "\n",
    "plt.subplot(222)\n",
    "plt.plot(x,stats.uniform.pdf(x,-5,10))\n",
    "plt.title('Uniform Distribution')\n",
    "\n",
    "plt.subplot(223)\n",
    "plt.plot(x[x > -1],stats.chi2.pdf(x[x>-1],3))\n",
    "plt.title('Chi2 Distribution')\n",
    "\n",
    "plt.subplot(224)\n",
    "plt.plot(x[x > -1],stats.lognorm.pdf(x[x > -1],3))\n",
    "plt.title('Logarithmic Distribution')\n",
    "\n",
    "plt.subplots_adjust(hspace=.5)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Central Limit Theorem\n",
    "\n",
    "To gain intuition about the normal distribution, you are going to learn about the central limit theorem. \n",
    "\n",
    "The basic principle is that you can start out with any type probability distribution and transform it into a normal distribution. But of course it's a little bit more complicated than that.\n",
    "\n",
    "You need to take samples from the probability distribution and then calculate the mean of each sample. You do this over and over again taking the mean of a random sample. The probability distribution of these means will be normal. \n",
    "\n",
    "First, you are going to go through an example to see how the central limit theorem works. Then you'll be provided with a function where you can play around with different probability distributions to convince yourself that the central limit theorem works."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An unknown probability distribution\n",
    "\n",
    "Here is a function that creates a probability distribution that you probably would not find in nature. Run the cell below to create the distribution and see a histogram of the population that you will draw random samples from."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def probabilities(sample_distribution, trials, num_bins):\n",
    "    \n",
    "    # array from 1 to sample_distribution\n",
    "    pers = np.arange(1,sample_distribution + 1,1)\n",
    "    \n",
    "    # calculate array of relative probabilities for each sample\n",
    "    lower = int(.35*len(pers))\n",
    "    middle = int(.2*len(pers))\n",
    "    upper = int(.40*len(pers))\n",
    "    extreme = len(pers) - (lower + middle + upper)\n",
    "    \n",
    "    prob = [1.0]*(lower) + [.5]*middle + [2.0]*upper + [.5]*extreme\n",
    "    \n",
    "    # normalize probability distribution\n",
    "    prob /= np.sum(prob)\n",
    "\n",
    "    # take a random sample for number of times in trials variable\n",
    "    probability_distribution = np.random.choice(pers, trials, p=prob)\n",
    "\n",
    "    # visualize distribution\n",
    "    plt.hist(probability_distribution, bins = num_bins)\n",
    "    plt.title('Histogram of the Population')\n",
    "    plt.xlabel('Value from the Population')\n",
    "    plt.ylabel('Count')\n",
    "    plt.show()\n",
    "    \n",
    "    # return random sample size of trials variable\n",
    "    return probability_distribution\n",
    "\n",
    "### create a distribution from the probabilities() function\n",
    "probability_distribution = probabilities(50,10000,100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The population of values definitely does not have a normal distribution. Run the next cell to calculate the mean of this population:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('population mean', 28.8748)\n"
     ]
    }
   ],
   "source": [
    "print('population mean', np.mean(probability_distribution))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Code for the Central Limit Theorem\n",
    "\n",
    "The code in the next cell is going to randomly take 10 samples from the distribution:\n",
    "\n",
    "```\n",
    "for sample in range(10):\n",
    "    samples.append(distribution[np.random.randint(1,len(distribution))])\n",
    "```\n",
    "\n",
    "and then calculate the mean of the samples.\n",
    "\n",
    "```\n",
    "sample_means.append(np.mean(samples))\n",
    "```\n",
    "\n",
    "Notice that the code is storing the mean of each set into the `sample_means` list.\n",
    "\n",
    "Then the code will repeat this process one-hundred thousand times storing every calculated mean into the `sample_means` list.\n",
    "\n",
    "Finally, the code will output a histogram of the original population alongside a histogram of the sample means. \n",
    "\n",
    "Run the code cell below to see the central limit theorem in action:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# take samples from the distribution and calculate the mean of each sample\n",
    "iterations = 100000\n",
    "num_samples = 10\n",
    "distribution = probability_distribution\n",
    "sample_means = []\n",
    "\n",
    "# iterate through picking samples and calculating the mean of each sample\n",
    "for iteration in range(iterations):\n",
    "\n",
    "    samples = []\n",
    "\n",
    "    # iterate through for the sample size chosen and randomly pick samples\n",
    "    for sample in range(num_samples):\n",
    "        samples.append(distribution[np.random.randint(1,len(distribution))])\n",
    "\n",
    "    # calculate the mean of the sample\n",
    "    sample_means.append(np.mean(samples))\n",
    "\n",
    "# Plot the distribution of the sample means alongside the population histogram\n",
    "ax1 = plt.subplot(121)\n",
    "plt.hist(distribution, bins=200)\n",
    "plt.title('Histogram of the Population')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Count')\n",
    "\n",
    "ax2 = plt.subplot(122, sharex=ax1, sharey=ax1)\n",
    "plt.hist(sample_means, bins=200)\n",
    "plt.title('Histogram of the Sample Means')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Count')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pretty amazing! Think about what this means. You started out with a population that did not look normal at all. You then took random samples with a size of 10, and then calculated the mean of the samples. You did this over and over again, and the distribution of the sample means looks normal. \n",
    "\n",
    "##### Increasing Sample Size\n",
    "Let's see what happens if the sample size goes up to 50. Run the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# take samples from the distribution and calculate the mean of each sample\n",
    "iterations = 100000\n",
    "num_samples = 50\n",
    "distribution = probability_distribution\n",
    "sample_means = []\n",
    "\n",
    "# iterate through picking samples and calculating the mean of each sample\n",
    "for iteration in range(iterations):\n",
    "\n",
    "    samples = []\n",
    "\n",
    "    # iterate through for the sample size chosen and randomly pick samples\n",
    "    for sample in range(num_samples):\n",
    "        samples.append(distribution[np.random.randint(1,len(distribution))])\n",
    "\n",
    "    # calculate the mean of the sample\n",
    "    sample_means.append(np.mean(samples))\n",
    "\n",
    "# Plot the distribution of the sample means alongside the population histogram\n",
    "ax3 = plt.subplot(121)\n",
    "plt.hist(distribution, bins=200)\n",
    "plt.title('Histogram of the Population')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Count')\n",
    "\n",
    "ax4 = plt.subplot(122, sharex=ax3, sharey=ax3)\n",
    "plt.hist(sample_means, bins=200)\n",
    "plt.title('Histogram of the Sample Means')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Count')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like the normal distribution got 'peakier' and the range of values on the x-axis got smaller. \n",
    "\n",
    "That's very interesting! As your sample size increases, it seems to be more likely that your sample mean will be close to the population mean, which was about 29. This makes sense intuitively. The population had 10,000 values in it. If your sample has 9,999 randomly chosen values, you'll get close to the actual mean. If you take 1 sample, it's very likely that your value is far from the mean.\n",
    "\n",
    "That is one reason why you might see recommendations to use at least 20, 30 or 50 samples when taking measurements and running experiments. The larger your sample size, the more likely it becomes that your sample mean is equal to the population mean."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Sample Means and the Normal Distribution\n",
    "\n",
    "To convince yourself that the new distribution is close to a normal distribution, you are going to output two more visualizations. \n",
    "\n",
    "The first visualization will adjust the distribution so that the area of all the bars adds up to 1. The chart will also show a normal distribution that has the same mean and standard deviation of the sample means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda2\\lib\\site-packages\\matplotlib\\axes\\_axes.py:6571: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
      "  warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n",
      "D:\\Anaconda2\\lib\\site-packages\\ipykernel_launcher.py:10: MatplotlibDeprecationWarning: scipy.stats.norm.pdf\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# normalized histogram of the sample means and an equivalent normal distribution with same mean and standard deviation \n",
    "fig = plt.figure(figsize=(8, 3)) \n",
    "\n",
    "plt.hist(sample_means, bins=50, normed=True)\n",
    "plt.title('Normalized Histogram of Sample Means and \\n Equivalent Normal Distribution')\n",
    "plt.xlabel('Value')\n",
    "plt.ylabel('Count')\n",
    "\n",
    "x = np.linspace(min(sample_means), max(sample_means), 1000)\n",
    "plt.plot(x,mlab.normpdf(x, np.mean(sample_means),np.std(sample_means)))    \n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution of the sample means looks pretty similar to the continuous normal distribution. \n",
    "\n",
    "Here is one more visualization to help convince you that the sample means distribution is getting close to normal. The following are [probability plots](http://www.itl.nist.gov/div898/handbook/eda/section3/normprpl.htm). The x-axis has the values from your distribution and the y-axis has ideal values if the distribution were normal. A completely normal distribution would therefore be a straight line. \n",
    "\n",
    "Run the code cell below to compare the probability plot of the population with the probability plot of the sample means. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Probability Plot of the Sample Means')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Compare population distribution with sample mean distribution\n",
    "\n",
    "fig = plt.figure(figsize=(8, 3)) \n",
    "\n",
    "ax5 = plt.subplot(121)\n",
    "stats.probplot(probability_distribution, plot=plt)\n",
    "ax6 = plt.subplot(122)\n",
    "stats.probplot(sample_means, plot=plt)\n",
    "\n",
    "ax5.set_title('Probability Plot of the Population')\n",
    "ax6.set_title('Probability Plot of the Sample Means')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So it looks like the distribution of the sample means (sample size was 30), is much closer to a normal distribution than the original population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Explore on Your Own\n",
    "\n",
    "Now you can convince yourself that different probability distributions still work with the central limit theorem.  Here are a set of functions to create different types of probability distributions. \n",
    "\n",
    "Make sure to run the cells below before trying to use these functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Probability distributions\n",
    "\n",
    "def random_uniform(low_value, high_value, num_samples):    \n",
    "    return np.random.uniform(low_value, high_value, num_samples)\n",
    "\n",
    "### Poisson Distribution\n",
    "def poisson_distribution(expectation, num_samples):\n",
    "    return np.random.poisson(expectation, num_samples)\n",
    "\n",
    "def binomial_distribution(result, probability, trials):\n",
    "    return np.random.binomial(result, probability, trials)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is some example code of how to create distributions from the functions given. These distributions will be your populations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "uniform = random_uniform(1, 5, 100000)\n",
    "poisson = poisson_distribution(6.0, 10000)\n",
    "binomial = binomial_distribution(1, 0.5, 10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've provided a function that does all of the central limit theorem analysis for you. The function below receives a probability distribution and then takes random samples over and over again. The mean of each sample is calculated, and then the resulting statistics and histograms are displayed. Run the code cell below to initialize the function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Shows Central Limit Theorem: takes samples from a distribution and calculates the mean of each sample. \n",
    "#\n",
    "# variables:\n",
    "# distribution => array containing values from a population\n",
    "# iterations => number of times to draw samples and calculate the mean of the sample\n",
    "# num_samples => sample size\n",
    "# num_bins => controls number of bins in the histograms3\n",
    "#\n",
    "# outputs:\n",
    "# (1) summary statistics of the population and the means of the samples\n",
    "# (2) histogram of the population and means of the samples\n",
    "# (3) normalized histogram of the means and line chart of equivalent normal distribution with same mean and stdeviation\n",
    "# (4) probability plot of the original distribution and the means of the samples\n",
    "#\n",
    "###\n",
    "\n",
    "def sample_means_calculator(distribution, iterations, num_samples, num_bins):\n",
    "    \n",
    "    # take samples from the distribution and calculate the mean of each sample\n",
    "    sample_means = []\n",
    "    \n",
    "    # iterate through picking samples and calculating the mean of each sample\n",
    "    for iteration in range(iterations):\n",
    "    \n",
    "        samples = []\n",
    "        \n",
    "        # iterate through for the sample size chosen and randomly pick samples\n",
    "        for sample in range(num_samples):\n",
    "            samples.append(distribution[np.random.randint(1,len(distribution))])\n",
    "    \n",
    "        # calculate the mean of the sample\n",
    "        sample_means.append(np.mean(samples))\n",
    "\n",
    "\n",
    "    # Calculate summary statistics for the population and the sample means\n",
    "    population_mean = np.average(distribution)\n",
    "    population_median = np.median(distribution)\n",
    "    population_deviation = np.std(distribution)\n",
    "        \n",
    "    sample_mean = np.mean(sample_means)\n",
    "    sample_median = np.median(sample_means)\n",
    "    sample_deviation = np.std(sample_means)\n",
    "\n",
    "    print('population mean ', population_mean, ' \\n population median ', population_median, '\\n population standard deviation ', population_deviation)\n",
    "    print('\\n mean of sample means ', sample_mean, '\\n median of sample means ', sample_median, '\\n standard deviation of sample means ', sample_deviation)\n",
    "    \n",
    "    # histogram of the population and histogram of sample means\n",
    "    fig = plt.figure(figsize=(8, 4)) \n",
    "\n",
    "    ax1 = plt.subplot(121)\n",
    "    plt.hist(distribution, bins=num_bins)\n",
    "    plt.title('Histogram of the Population')\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Count')\n",
    "    \n",
    "    ax2 = plt.subplot(122, sharex=ax1, sharey=ax1)\n",
    "    plt.hist(sample_means, bins=num_bins)\n",
    "    plt.title('Histogram of the Sample Means')\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Count')\n",
    "        \n",
    "    plt.show()\n",
    "    \n",
    "    # normalized histogram of the sample means and an equivalent normal distribution with same mean and standard deviation \n",
    "    fig = plt.figure(figsize=(8, 3)) \n",
    "\n",
    "    plt.hist(sample_means, bins=num_bins, normed=True)\n",
    "    plt.title('Normalized Histogram of Sample Means and \\n Equivalent Normal Distribution')\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Count')\n",
    "\n",
    "    x = np.linspace(min(sample_means), max(sample_means), 1000)\n",
    "    plt.plot(x,mlab.normpdf(x, sample_mean, sample_deviation))    \n",
    "    \n",
    "    plt.show()\n",
    "    \n",
    "    # probability plots showing how the sample mean distribution is more normal than the population mean\n",
    "    fig = plt.figure(figsize=(8, 3)) \n",
    "   \n",
    "    ax5 = plt.subplot(121)\n",
    "    stats.probplot(distribution, plot=plt)\n",
    "    ax6 = plt.subplot(122)\n",
    "    stats.probplot(sample_means, plot=plt)\n",
    "    \n",
    "    ax5.set_title('Probability Plot of the Population')\n",
    "    ax6.set_title('Probability Plot of the Sample Means')\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you can call the function like this:\n",
    "\n",
    "`sample_means_calculator(distribution, iterations, num_samples, num_bins)`\n",
    "\n",
    "Run the code cell below to see how the function works. The distribution variable is a population distribution. Iterations is how many times you want to sample the population. Num_samples is the sample size. And num_bins says how many bins to use for the histogram output.\n",
    "\n",
    "It might take a minute or so to get the output depending on the size of your population, the sample size for showing the central limit theorem, etc. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('population mean ', 2.998108921993986, ' \\n population median ', 2.997052842735356, '\\n population standard deviation ', 1.1555061390227697)\n",
      "('\\n mean of sample means ', 2.998355011711505, '\\n median of sample means ', 2.9979887553582127, '\\n standard deviation of sample means ', 0.16328540286537035)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda2\\lib\\site-packages\\ipykernel_launcher.py:73: MatplotlibDeprecationWarning: scipy.stats.norm.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Take samples and calculate the sample means for central limit theorem\n",
    "sample_means_calculator(uniform, 100000, 50, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Your Turn\n",
    "\n",
    "Now it's your turn to try different probability distributions and see the outcome. We have provided three functions that you can play around with for creating your population values. Feel free to create other types of distributions until you've convinced yourself that the central limit theorem works. Try adjusting the population distributions, the sample sizes, the number of iterations, etc. \n",
    "\n",
    "Here is some code to help you get started. Try changing the sample size, for example, to see how sample size affects results. What about the number of iterations, which controls the number of samples that will be taken from the population?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### Sample Code\n",
    "# sample_means_calculator(random_uniform(1,10,100000), 10000, 50, 100)\n",
    "# sample_means_calculator(poisson_distribution(6.0,500000), 10000, 90, 100)\n",
    "# sample_means_calculator(binomial_distribution(1, 0.5, 10000), 10000, 200, 100)\n",
    "#\n",
    "# sample_means_calculator(distribution, number_of_iterations, sample_size, histogram_bins)\n",
    "#\n",
    "###\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gaussian_density(x, mu, sigma):\n",
    "    return (1/np.sqrt(2*np.pi*np.power(sigma, 2.))) * np.exp(-np.power(x - mu, 2.) / (2 * np.power(sigma, 2.)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "def gaussian_probability(mean, stdev, x_low, x_high):\n",
    "    return norm(loc = mean, scale = stdev).cdf(x_high) - norm(loc = mean, scale = stdev).cdf(x_low)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
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